On Estimation of Functions of a Parameter Observed in Gaussian Noise
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The main problem of the paper looks as follows. A functional parameter θ ∈ Θ ⊂ L2(−∞,∞) is observed in Gaussian noise. The problem is to estimate the value F(θ) of a given function F. A construction of asymptotically efficient estimates for F(θ) is suggested under the condition that Θ admits approximations by subspaces HT ⊂ L2 with reproducing kernels KT (t, s), KT (t, t) ≤ T.
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